Maintaining constraints across different databases

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What are the different approaches to maintain constraints accross different databases? what are the pro's and con;s of the process, If creating constraints is not possible, what is the best way of doing it?
I was also wondering if there is a possibility that, we create a trigger on a datasbase table A residing in the database 1 To insert a new record in the table B in the database 2, When ever there is a new record in the table A?